Abstract :
Long-range quantum entanglement is now understood to be a fundamental
characteristic of exotic states of quantum matter with an energy gap to all
excitations: these include the fractional quantum Hall states found at very
high magnetic fields, and certain insulators with possible spin-liquid states.
However, such entanglement can also be present

in
gapless, conducting states of matter (‘metals’ ) found under more ordinary
conditions. I will describe recent experiments

on the cuprate compounds, and on graphene,
which are consistent with the presence of novel metallic states with